Estimating the smoothing parameter in generalized spline-based regression: II. Empirical and fully Bayesian approaches. Experiences with Gibbs sampling in simulated results
[For part I of this paper see the preceding entry, Zbl 1007.62036] A nonparametric regression model is considered with binary or Gaussian responses where the expectation of the data is a smooth function of the covariates. A spline technique is used for estimation of this function. The author interprets the standard cross-validation approach for choice of the smoothing parameter as an empirical Bayes one and develops a fully Bayesian approach based on an improper prior \(p(h/\gamma^2)\propto\exp(-\gamma^{-2}J(h))\) on the space of possible regression functions \(h\), where \(J\) is a roughness penalty and the smoothing parameter \(\gamma^{-2}\) is considered as a hyperparameter. In the examples the distribution of \(\gamma^{-2}\) is taken as Gamma or Pareto. Results of simulations are presented for quadratic and quadratic \(+\) sinusoidal functions \(h\).
scientific article; zbMATH DE number 1878600